Temperature dependent direct-bandgap light emission and optical gain of Ge

Band structure, electron distribution, direct-bandgap light emission, and optical gain of tensile strained, n-doped Ge at different temperatures were calculated. We found that the heating effects not only increase the electron occupancy rate in the Gamma valley of Ge by thermal excitation, but also reduce the energy difference between its Gamma valley and L valley. However, the light emission enhancement of Ge induced by the heating effects is weakened with increasing tensile strain and n-doping concentration. This phenomenon could be explained by that Ge is more similar to a direct bandgap material under tensile strain and n-doping. The heating effects also increase the optical gain of tensile strained, n-doped Ge at low temperature, but decrease it at high temperature. At high temperature, the hole and electron distributions become more flat, which prevent obtaining higher optical gain. Meanwhile, the heating effects also increase the free-carrier absorption. Therefore, to obtain a higher net maximum gain, the tensile strained, n-doped Ge films on Si should balance the gain increased by the heating effects and the optical loss induced by the free-carrier absorption.